There are a few ways to do this, in the attached I demonstrated two of them using the Superstore Sales data, with Sub-Category as a stand-in for Item. In the first method a parameter is used to choose the sub-category, and a calculated field is used to return the date if the chosen parameter is the sub-category, which is then compared to the overal minimum. In this view, the Sub-Category is not on Columns, Rows, or the Marks Card.

The second method uses table calculations, and has Sub-Category in the view. For this, a table calculation filter is used to pick the sub-category of interest, a second table calculation identifies the minimum order date across all sub-categories, and a third table calculation uses the second to only filter for the first orders.